Journal of Symbolic Computation - Special issue on computational algebraic complexity
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Algorithms for computer algebra
Algorithms for computer algebra
Efficient rational number reconstruction
Journal of Symbolic Computation
Modern computer algebra
On Euclid's Algorithm and the Theory of Subresultants
Journal of the ACM (JACM)
The Calculation of Multivariate Polynomial Resultants
Journal of the ACM (JACM)
Algebraic factoring and rational function integration
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Maximal quotient rational reconstruction: an almost optimal algorithm for rational reconstruction
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
P-adic reconstruction of rational numbers
ACM SIGSAM Bulletin
A complete modular resultant algorithm targeted for realization on graphics hardware
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Modular resultant algorithm for graphics processors
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
Computing resultants on Graphics Processing Units: Towards GPU-accelerated computer algebra
Journal of Parallel and Distributed Computing
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Let A and B be two polynomials in ℤ [x,y] and let R = resx(A,B) denote the resultant of A and B taken wrt x. In this paper we modify Collins' modular algorithm for computing R to make it output sensitive. The advantage of our algorithm is that it will be faster when the bounds needed by Collins' algorithm for the coefficients of R and for the degree of R are inaccurate. Our second contribution is an output sensitive modular algorithm for computing the monic resultant in ℚ[y]. The advantage of this algorithm is that it is faster still when the resultant has a large integer content. Both of our algorithms are necessarily probabilistic.The paper includes a number of resultant problems that motivate the need to consider such algorithms. We have implemented our algorithms in Maple. We have also implemented Collins' algorithm and the subresultant algorithm in Maple for comparison. The timings we obtain demonstrate that a good speedup is obtained.